35x^2-7=14

Solution for 35x^2-7=14 equation:

35x^2-7=14

We move all terms to the left:

35x^2-7-(14)=0

We add all the numbers together, and all the variables

35x^2-21=0

a = 35; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·35·(-21)
Δ = 2940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{15}}{2*35}=\frac{0-14\sqrt{15}}{70}
=-\frac{14\sqrt{15}}{70}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{15}}{2*35}=\frac{0+14\sqrt{15}}{70}
=\frac{14\sqrt{15}}{70}
=\frac{\sqrt{15}}{5}
$